Simulation and Modeling: Understanding System Behavior through Imitation, Study notes of Mathematical Modeling and Simulation

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mulation and Modeling

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Prof. S.Shakya

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mulation and Modeling

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Introduction to Modeling and simulation

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System



The term system is derive from the Greek word systema,which means an organized relationship among functioningunits or componentsunits or components. 

System exists because it is designed to achieve one or moreobjectives.We come into daily contact with the transportation system 

We

come into daily contact with the transportation system,

the telephone system, the accounting system, the productionsystem, and for two decades the computer system. 

There are more than a hundred definitions of the word 

There are more than a hundred definitions of the wordsystem, but most seem to have a common thread thatsuggests that a system is an orderly grouping ofinterdependent components linked together according to a

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plan to achieve a specific objective.

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System

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Klir

• gives a collection of 24 definitions one such



Klir

gives a collection of 24 definitions one such

definition is “ A system is a collection ofcomponents wherein individual components are

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constrained by connecting interrelationships suchthat the system as a whole fulfills some specificfunctions in response to varying demands” *Klir, George J. , an approach to general systems

theory New York: Van Nostrand Reinhold Cotheory, New York: Van Nostrand Reinhold Co, 1969

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ome keywords to know …

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System

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is a collection of entities that act and interact together toward the accomplishment of somelogical end (computer, network, communication

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systems, queuing systems etc.)

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Simulation 

It is an experiment in a computer where the realsystem is replaced by the execution of theprogram 

It is a program that mimics (imitate) the behaviourof the real systemof the real system

Introduction

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ystem

· A system exists and operates in time and space. 

Model · A model is a simplified representation of a system at

some particular point in time or space intended tosome particular point in time or space intended topromote understanding of the real system. 

Simulation · A simulation is the manipulation of a model in such a

way that it operates on time or space to compress it,way that it operates on time or space to compress it,thus enabling one to perceive the interactions thatwould not otherwise be apparent because of theirseparation in time or space.

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separation in time or space.

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Models of the system

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Real System (Motherboard)

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Models of the System

Concept of Simulation

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Simulation is the representation of a real life 

Simulation

is the representation of a real life

system by another system, which depicts theimportant characteristics of the real system and

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allows experimentation on it. 

In another word simulation is an imitation of thereality.

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Simulation has long been used by theresearchers, analysts, designers and otherprofessionals in the physical and non physicalprofessionals in the physical and non-physicalexperimentations and investigations.

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Why Simulate?Why

Simulate?

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It may be too difficult, hazardous, or expensive to observe a real,

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operational system 

Parts of the system may not be observable (e.g., internals of asilicon chip or biological system) Uses of simulations 

Analyze systems before they are built 

Analyze systems before they are built 

Reduce number of design mistakes 

Optimize design



Analyze operational systems 

Analyze operational systems 

Create virtual environments for training, entertainment

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ypes of Simulation Models

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ystem model

deterministic

stochastic

static

dynamic

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dynamic

Monte Carlo

continuous

discrete

continuous

discrete

simulation

Discrete-event

simulation

Continuoussimulation

Discrete-event

simulation

Continuoussimulation

Types of Simulation Models ^

Simulation models can be classified as being static ordynamic, deterministic or stochastic and discrete orcontinuouscontinuous. 

A static simulation model represents a system, which doesnot change with time or represents the system at a particularpoint in time.p 

Dynamic simulation models represent systems as theychange over time. 

Deterministic models have a known set of inputs, which

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result into unique set of outputs. 

In stochastic model, there are one or more random inputvariables, which lead to random outputs. 

System in which the state of the system changescontinuously with time are called continuous systems whilethe systems in which the state changes abruptly at discrete

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points in time called discrete systems.